The first ever fully three-dimensional magnetohydrodynamic (MHD) simulations of the detailed effects of MHD discontinuities on the magnetosheath have been performed. The simulation results predict that the interaction between a rotational discontinuity (RD) and the bo it shock produces an MHD wave pulse that propagates downstream from the bow shock to the magnetopause. The main components of this pulse are two slow shocks sandwiched between two time-dependent intermediate shocks; in perfectly ideal MHD, these shocks would presumably resolve into slow shocks sandwiched between two RDs. Inside the pulse, the plasma density, thermal pressure, dynamic pressure (rho v(2)), and total pressure all increase, while the magnetic field magnitude decreases; The pulse convects with the downstream flow through the magnetosheath at a speed that is markedly slower than that of the original RD. It comes to rest on the magnetopause, where it raises the total pressure by as much as 75% in some locations. The pulse eventually disappears, as it is convected away by the solar wind flow around the magnetopause. The pulse remains in the magnetosheath for a few Alfven times (i.e., solar wind Alfven velocity divided by the Earth's radius, perhaps 1-3 min depending on the actual solar wind parameters) after the initial RD has propagated downstream past the magnetopause. Comparisons are made with previous one-dimensional and two-dimensional studies of this problem. We conclude that the pulses seen in these simulations are possible causes of magnetic impulse events observed in the ionosphere and slow mode structures observed in the inner subsolar magnetosheath.